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ON POINTS WITH POSITIVE DENSITY OF THE DIGIT SEQUENCE IN INFINITE ITERATED FUNCTION SYSTEMS
Published online by Cambridge University Press: 09 September 2016
Abstract
Let $\{f_{n}\}_{n\geq 1}$ be an infinite iterated function system on
$[0,1]$ and let
$\unicode[STIX]{x1D6EC}$ be its attractor. Then, for any
$x\in \unicode[STIX]{x1D6EC}$, it corresponds to a sequence of integers
$\{a_{n}(x)\}_{n\geq 1}$, called the digit sequence of
$x$, in the sense that
$$\begin{eqnarray}x=\lim _{n\rightarrow \infty }f_{a_{1}(x)}\circ \cdots \circ f_{a_{n}(x)}(1).\end{eqnarray}$$
MSC classification
- Type
- Research Article
- Information
- Copyright
- © 2016 Australian Mathematical Publishing Association Inc.
Footnotes
This work was supported by the Fundamental Research Funds for the Central University (Grant No. 2662015QC001) and NSFC (Grant Nos. 11426111 and 11501168).
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